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Intro:
I found this strange, tattered journal while walking through the woods behind my house, and wondered if you could make sense of it all. From what I could glean, it was written by a nomadic tribe, but none of this is really given.

Notes:
I have managed to find a psychic of rather ill-repute, who turned out to be outstanding at her job, and managed to get in contact with my crazy uncle, who had been working on deciphering the text before me. Here is the revised edition of the text. Now, to head home and take care of that wolf bite. My fur's itching like crazy...

The Riddle:

Searching, squaring, measuring, squeezing,
it's a measurement.
Not the worst, I end up choosing,
lemmings know the rest.

It saddens my heart to relay this next part:
Swear not in vain, or swallow the pain.
With his head now gone, the ill-begotten son's song,
ended with keen notes of grieving.

Three's fourteen, the next sign read,
and most of us waved goodbye.
The rest of us spoke out our puzzlement,
and headed off with a sigh.

Be forewarned, your journey be done,
once you've followed our story.
Our strange sense of pride, and
the cause of our tribe's
pilgrimage to seas unknown.
So, if you be brave,
Take heed, my friend,
and learn this lesson from our passage...

Make right from our wrongs, and carry our songs,
to the pages of some dusty story/novel.

History:
My Uncle was secretly following the stories of a small indigenous group of people that inhabited a remote corner of the earth some 2000 years ago, trying to figure out their entire history after stumbling upon some dusty old journal at a local bazaar. He always thought of it as merely a way to keep time and wile away boredom, but began to wonder whether the stories were true, how this tribe had lived, and where they had gone. He spent nearly every waking moment of his last 10 years trying to search for some final clue, when he stumbled upon this inscription carved in a deep cavern by long-forgotten hands, written in some strange dialect. However, he could never finish the decipher.

Directions:
Please, puzzlers, can you solve this puzzle, and finally let my Uncle find the rest he deserves? You are my last hope, for I fear I am growing mad myself (see my previous renditions of this story to find out how).

IMPORTANT NOTES:
Several people are of the mistaken impression that the answer has to do with math.
Also, partial answers are heavily encouraged.

Hint 1:

Stanza 1
I found some hidden edits made with a tincture of foxbane and the light of a blue moon while perusing the riddle once more: the words the rest are highlighted, and it appears as if a dot was made above the comma in line 3. It also appears as if line 2 was scribbled in at a later date...

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  • $\begingroup$ like my others, parts of this play like a cryptic crossword, where I offer directions for hints or words. $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 15:07
  • 1
    $\begingroup$ Just caught a quick typo, so I patched it up. :) I'm sure this is just as impossible as your other riddles, but I'll work on it! $\endgroup$
    – Bailey M
    Commented Jul 13, 2015 at 15:17
  • $\begingroup$ Maybe. The whole trick is to think of each stanza as a separate puzzle, then work from there. You might need to know a little programming for the last word, but I'm sure you can manage!! Also: I love compounding words together, because it helps me work out a riddle, but this one requires less manipulation than my others. $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 15:20
  • $\begingroup$ Note: the "puzzling phrase" is because the answer will probably sound like gibberish when you think about it, but be pretty fun besides! $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 15:32
  • $\begingroup$ Feel free to ask questions in the comments below, and supply partial answers: once you've figured out the trick, the rest should be easy to solve. $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 18:47

2 Answers 2

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They were trying to:

Square the circle - https://en.wikipedia.org/wiki/Squaring_the_circle

References in the riddle:

'Searching, squaring, measuring, squeezing' - The most common attempts to approximate $\pi$ have involved calculating increasingly precise upper and lower bounds.

'with a swear yelled in vain, the ill-begotten's sheep was slain' - After many many failed attempts, it has since been proven that because $\pi$ is transcendental, it's precise value cannot be obtained using a straight-edge and compass.

'Three's fourteen' - 3.14 is perhaps the most common numerical approximation of pi used in conversation.

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  • $\begingroup$ You are right about pi - from a programming perspective, 3.14 is the 14th element of an array labeled "3", hence 3's fourteen. However, the rest is wrong. $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 19:17
  • $\begingroup$ Remember, every line but the ones I specified are used in the solution/explanation. You seem to be thinking a little too out of the circle ;p $\endgroup$
    – Nyk 232
    Commented Jul 13, 2015 at 19:18
  • $\begingroup$ @Nyk232 in a programming perspective wouldn't it have to be three[13] to access three's fourteenth element? - As a number can't be a variable name, and they use 0 base indexing. (3.14 would just be interpreted as a float otherwise) $\endgroup$
    – Mark N
    Commented Jul 14, 2015 at 15:59
  • $\begingroup$ @MarkN ah, this page shows that some languages use base 0, not base 1! I'm glad you pointed that out, though. $\endgroup$
    – Nyk 232
    Commented Jul 14, 2015 at 16:13
  • $\begingroup$ @markN Furthermore, at least in C++/C# you can #define 3 = int[14]; or so I think - I really don't want to break my computer trying so!! $\endgroup$
    – Nyk 232
    Commented Jul 14, 2015 at 16:15
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They were trying to

Decree the estimate of pi.

Searching, squaring, measuring, squeezing,

These are ways to estimating something -> Estimate

the path swaps next, with groups of best, the last leader's final decision.

Last leader's final decision: decree. Estimate decree => Decree estimate.

It shatters my heart, to relay this next part: with a swear yelled in vain, the ill-begotten's sheep was slain.

A swear yelled in vain: Oh f**k! This leads to: oh f => of

Three's fourteen, the next sign reads,

Pi. I have added the the as addition, not something I could get from the puzzle.

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  • $\begingroup$ well, you are right in your approach, but not in your decisions, grasshopper. NOTE for future puzzling afficianados: the answer DOES NOT have to do with math, unless you count the synonym of measuring used as the first word, or if SIZE MATTERS. $\endgroup$
    – Nyk 232
    Commented Sep 4, 2015 at 1:52

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